Proposition Replicated
Proposition II.4
If a straight line be cut at random, the square on the whole is equal to the squares on the segments and twice the rectangle contained by the segments.
01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:II.4
Euclid's Elements, encoded as an rrxiv paper
Blaise Albis-Burdige, Claude·2605.00009·math.HO, math.MG, math.NT
Neighborhood at a glance
Full neighborhood
Depends on (7)
- I.5Proposition I.5In isosceles triangles the angles at the base are equal to one another; and if the equal straight lines be produced…
- I.6Proposition I.6If in a triangle two angles are equal to one another, the sides which subtend the equal angles will also be equal to…
- I.29Proposition I.29A straight line falling on parallel straight lines makes the alternate angles equal to one another, the exterior angle…
- I.31Proposition I.31Through a given point to draw a straight line parallel to a given straight line.
- I.34Proposition I.34In parallelogrammic areas the opposite sides and angles are equal to one another, and the diameter bisects the areas.
- I.43Proposition I.43In any parallelogram the complements of the parallelograms about the diameter are equal to one another.
- I.46Proposition I.46On a given straight line to describe a square.
Required by (dependents) (4)
- II.7Proposition II.7If a straight line be cut at random, the square on the whole and that on one of the segments both together are equal to…
- II.8Proposition II.8If a straight line be cut at random, four times the rectangle contained by the whole and one of the segments together…
- II.12Proposition II.12In obtuse-angled triangles the square on the side subtending the obtuse angle is greater than the squares on the sides…
- XIII.4Proposition XIII.4If a straight line be cut in extreme and mean ratio, the square on the whole and the square on the lesser segment…
Discussion
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